The value of a particular model of car, $£V\pounds V$ , when it is $t\,$ years old is modelled by

$V = ab^{t}$

where $a\,$ and $b\,$ are constants.

A dealer records the value of a number of these cars of different ages. The data are coded using $y = \log_{10} V$ , and the regression line of $y\,$ on $t\,$ is found to be

$y = 4.28 - 0.0862 t$

Express $V\,$ in the form $Ae^{-kt}$ , where $A\,$ and $k\,$ are positive constants. Give the values of $A\,$ and $k\,$ to 3 significant figures.

Using this model, find how long it takes for the value of one of these cars to fall to one third of its value when new. Give your answer to the nearest month.

The value of a particular model of car, $£V\pounds V$ , when it is $t\,$ years old is modelled by

$V = ab^{t}$

where $a\,$ and $b\,$ are constants.

A dealer records the value of a number of these cars of different ages. The data are coded using $y = \log_{10} V$ , and the regression line of $y\,$ on $t\,$ is found to be

$y = 4.28 - 0.0862 t$

Express $V\,$ in the form $Ae^{-kt}$ , where $A\,$ and $k\,$ are positive constants. Give the values of $A\,$ and $k\,$ to 3 significant figures.

Using this model, find how long it takes for the value of one of these cars to fall to one third of its value when new. Give your answer to the nearest month.

2 Statistics

Question 46

Markscheme

2 Statistics

Question 46

Markscheme

2 Statistics

Question 46

2 Statistics Questions

2 Statistics

Question 46

2 Statistics Questions